Validation of CO 4th positive radiation for Mars entry

Journal of Quantitative Spectroscopy & Radiative Transfer 121 (2013) 91–104

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Validation of CO 4th positive radiation for Mars entry A.M. Brandis a,n,1, C.O. Johnston b, B.A. Cruden c, D.K. Prabhu c, A.A. Wray d, Y. Liu d, D.W. Schwenke d, D. Bose d a

University Affiliated Research Center with University of California Santa Cruz, Mountain View, CA 94035, USA NASA Langley Research Center, Hampton, VA 23669, USA ERC Corporation, Mountain View, CA 94035, USA d NASA Ames Research Center, Mountain View, CA 94035, USA b c

a r t i c l e i n f o

abstract

Article history: Received 20 August 2012 Received in revised form 1 February 2013 Accepted 5 February 2013 Available online 19 February 2013

This paper presents measurements and simulations of CO 4th Positive equilibrium radiation obtained in the NASA Ames Research Center’s Electric Arc Shock Tube (EAST) facility. The experiments were aimed at measuring the level of radiation encountered during conditions relevant to high-speed entry into a simulated Martian atmosphere (96% CO2: 4% N2). The facility was configured to target several ranges of nominal Mars entry conditions, of which 7.35 km/s at 0.1 Torr (13.3 Pa), 6.2–8 km/s at 0.25 Torr (33 Pa) and 7.1–7.8 km/s at 1 Torr (133 Pa) are examined in this paper. The CO 4th Positive system was chosen to be the focus of this study as it accounts for a large percentage of the emitted radiation for Martian entry, and also due to the difficulties of obtaining experimental validation data due to the emission appearing in the Vacuum Ultra Violet (VUV) spectral range. The focus of this paper is to provide a comprehensive comparison between the EAST data and various CO 4th Positive databases available in the literature. The analysis endeavors to provide a better understanding of the uncertainty in the measurements and quantifies the level of agreement found between simulations and experimental data. The results of the analysis show that the magnitude of the CO 4th Positive radiative intensity is very sensitive to the flow temperature. Subsequently, simulations using thermodynamic equilibrium generally under-predict the experimental data by approximately a factor of up to 2. However, when simulations are performed using a flow temperature extracted from the black body limited portion of the CO 4th Positive spectra taken from experiment, the agreement between the EAST data and simulations is generally very good. Furthermore, comparisons of experimental data and simulations across other spectral regions provide additional support for the use of the black body temperature. & 2013 Elsevier Ltd. All rights reserved.

Keywords: CO 4th positive Radiation Validation Spectroscopic database Shock tube Mars

1. Introduction The radiative component of the heat flux encountered by previous vehicles entering the Martian atmosphere has generally been negligible. However, due to future n

Corresponding author. Tel.: þ1 6506040888. E-mail address: [email protected] (A.M. Brandis). 1 Currently employed at ERC Corporation, Mountain View, CA, 94035, USA. 0022-4073/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jqsrt.2013.02.009

potential missions involving large landers and high speed entry, interest in radiative heating has recently arisen for Martian entry conditions. Detailed simulations and experiments have been undertaken to quantify this radiation and associated uncertainties [1,2]. Understanding these uncertainties may influence future margin policies [3], and hence the thermal protection system (TPS) selection and thickness. The present analysis attempts to provide insight into the accuracy of theoretical models, and provide the first validation of CO 4th Positive

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measurements performed at conditions relevant to Martian entry. The significance of CO 4th Positive radiation is highlighted in Fig. 1, where it can be seen that this single system alone contributes approximately 65% of the total radiance at 7.96 km/s and 0.25 Torr. Furthermore, a significant portion of the CO 4th Positive intensity is optically thick, as can be seen in Fig. 2, where the intensity calculated without self-absorption is several orders of magnitude greater than the intensity calculated with self-absorption. As the absolute intensity level of CO 4th Positive is black body limited, the intensity dependence on temperature is particularly strong for two reasons. First, the CO 4th Positive emission increases with increasing temperature, and second, as the temperature increases the black body limit increases substantially in the VUV, therefore allowing greater levels of radiative intensity to be observed. This work will comprise of spectral comparisons with predictive modelling tools simulating the CO 4th Positive data as measured in the EAST facility. Furthermore, various sources of CO 4th Positive oscillator strengths will

Fig. 1. NEQAIR calculated spectrum for Mars entry at 7.96 km/s and 0.25 Torr highlighting contribution from CO 4th Positive.

be analysed and compared against EAST data. Fig. 2 also details the band head locations and shows that the comparisons presented in this paper provide a validation of the CO 4th Positive databases for a Dn ¼ 4 and lower as the transitions from a Dn ¼ 3 and higher are completely black body limited.

2. Description of the EAST facility The EAST facility at NASA Ames Research Center was developed to simulate high-enthalpy, ‘‘real gas’’ phenomena encountered by hypersonic vehicles entering planetary atmospheres. Experiments are performed to match flow parameters relevant to flight, such as velocity, static pressure, and atmospheric composition. The basic principle behind testing in the EAST facility is that the shockheated test gas in a shock tube simulates conditions behind the bow shock on a re-entry vehicle. It has the capability of producing superorbital shock speeds using an electric arc driver with a driven tube diameter of 10.16 cm [4]. The region of valid test gas lies between the shock front and the contact surface that separates the driver and driven gases. The test duration is defined as the axial distance between these two points divided by the local shock velocity. The characteristics of the EAST arc driver typically result in test times of approximately 4210 ms. Though short, this test time is often sufficient to capture the peak of the nonequilibrium shock radiation and the decay to equilibrium conditions. As the shocked gas arrives at the location of the test section in the tube, spectrometers attached to Charge Coupled Devices (CCDs) are gated and the spectral and spatial emission of the gas is analysed. EAST utilises four spectrometers per shot, associated with four different wavelength ranges. These cameras are referred to as: VUV (  1202215 nm), UV/Vis (  190 nm2500 nm), Vis/NIR (  480 nm2900 nm) and IR (  700 nm21650 nm). Since the intent of this paper is to examine CO 4th Positive emission, the study will focus predominantly on results from the VUV camera. The composition of the Mars like test gas used during the EAST testing was 96% CO2 and 4% N2. The experimental campaign was designed to be representative of highspeed entry into Mars’ atmosphere, with conditions examined in this paper covering 7.35 km/s at 0.1 Torr, 6.2–8 km/s at 0.25 Torr and 7.1–7.8 km/s at 1 Torr.

3. Description of predictive codes and databases Simulations were conducted with three separate radiation codes, NEQAIR [5], HARA [6,7] and HyperRad [8]. The process for conducting the simulations is to perform the calculation at a very high spectral resolution followed by a convolution (scan) with a slit function. The slit function is a combination of a Lorentzian and Gaussian function that has been fit to the corresponding measured instrument line shape2 [9]. Fig. 2. CO 4th Positive intensity calculated by NEQAIR using the Rodio and Hassan data with and without self-absorption (path length ¼ 10.16 cm). Band head locations are also shown. 6.44 km/s and 0.25 Torr.

2 The slit function fit parameters are available online by contacting the authors.

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3.1. NEQAIR code NEQAIR is a line-by-line radiation code, the name of which stands for Nonequilibrium Air Radiation [5]. NEQAIR computes spontaneous emission, absorption and stimulated emission due to transitions between various energy states of chemical species along a line-of-sight. Individual electronic transitions are considered for atoms and molecules, with the molecular band systems being resolved for each rotational line. More detail about NEQAIR can be found in Whiting et al. [5]. 3.2. HARA code The HARA radiation model applied in the present study is discussed in detail by Johnston et al. [6,7]. This model is based on a set of atomic levels and lines obtained from the National Institute of Standards and Technology (NIST) [10] and Opacity Project databases [11]. The atomic bound-free model is composed of cross sections from the Opacity project’s online TOPbase [12], which were curve fit by Johnston [6]. As CO 4th Positive is optically thick, a line-by-line approach for molecular radiation has been implemented into HARA. 3.3. HyperRad code HyperRad is a radiation code being developed at NASA Ames Research Center to compute fully coupled radiative heating of the gas and body surfaces in hypersonic flow and to provide spectra for comparison to experimental and flight data [8]. The reason for the development of HyperRad is to extend and update the physics utilised in codes such as NEQAIR and HARA and to include data from recent ab initio calculations. The physics-based modelling for energy state populations implemented in HyperRad uses coupled thermal, chemical, and radiative nonequilibria and is designed for high-end computing in terms of efficiency and parallelisation. An efficient and accurate, linelistdriven database has been implemented that contains data merged from NIST [10], TopBase [12] and Vanderbilt [13] atomic line datasets. The database currently includes C, C þ , þ N, N þ , O, O þ ; and the molecular band systems N2, O2, N2 , þ NO, C2, CO, CO , CN, C3, CO2, C2H. Ab initio calculations are used for electric dipole and quadrupole, magnetic dipole, and spin-forbidden transitions which include fine structure, pre-dissociation, and nonadiabatic corrections. The line broadening and shifts due to the Stark effect are based on computed rate coefficients and the linewidths have been parameterised up to a temperature of 50,000 K. More details regarding the development of the HyperRad code and database will be presented in upcoming publications. 3.4. NEQAIR and HARA comparison Fig. 3 shows a comparison of the NEQAIR and HARA codes using the CO 4th Positive data compiled by Babou et al. [14]. HyperRad is not shown here because it uses its own database. It can be seen that both codes produce very similar spectra and integrated radiance (a difference of

Fig. 3. Comparison of CO 4th Positive calculated by NEQAIR and HARA using the Babou et al. data at 6.45 km/s and 0.25 Torr.

less than 1%) when using the same database. As the differences between the two codes are small, this paper will not focus on comparing calculations performed with either NEQAIR or HARA, but rather on the different databases used for CO 4th Positive that could be implemented into either code. Three different databases are used with NEQAIR and HARA, as discussed below, while HyperRad employs its own newly developed ab initio database. 3.5. Overview of CO 4th positive models Various CO 4th Positive databases have been implemented into both NEQAIR and HARA for the purposes of comparison with EAST. The CO 4th Positive databases used in this paper have been compiled by Rodio and Hassan [15–17], Babou et al. [14] and da Silva and Dudeck [18]. The methodologies for calculating the spectroscopic data are similar in all three cases. Each method involves calculating ¨ Franck–Condon factors (FCFs) and Honl-London factors within the Born–Oppenheimer approximation [19]. However, there are differences between the methods. For example, Rodio and Hassan use the R-centroid approximation while Babou et al. and da Silva and Dudeck take into account the dependency of the Electronic Transition Moment Function (ETMF) on the inter nuclei distance. Furthermore, there are differences in the various sources of literature used for the calculation of the spectroscopic data. Two such differences relate to the method used for calculating the potential energy curves and the choice in the source of data used for the ETMF. In terms of calculation of the potential energy curves, Rodio and Hassan implement a five parameter Hulburt–Hirschfelder potential [20], whereas both Babou et al. and da Silva and Dudeck use the Rydberg– Klein–Rees (RKR) [21–23] procedure. In terms of the choice of ETMF implemented, Babou et al. use the ab initio ETMF developed by Kirby and Cooper [24], while da Silva and Dudeck, and Rodio and Hassan use the experimentally based ETMF developed by DeLeon [25]. In terms of the calculation of CO 4th Positive emission with HyperRad, the theoretical spectrum is based on high quality ab initio potential energy curves and transition moments computed using the Molpro program [26].

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The ab initio calculations utilised the cc-pV5Z [27] one electron basis set augmented by the correlating functions and diffuse basis functions as advocated by Schwenke [28]. The molecular orbitals were generated by the complete active space method using the valence active space and weighted averages of various energy states. These weights were dynamically determined as described by Deskevich et al. [29]. The final energies and transition moments were computed using the averaged coupled pair functional method correlating all electrons. The rovibrational energy levels and transition energies were computed using the code previously described by Schwenke [30]. To improve the agreement with experimental measurements, the B1 P potential was shifted downwards by 120 cm  1 to make the computed and measured n ¼ 2 and J¼1 energy the same. The measured energy is 67 678.92 cm  1, so the adjustment is less than 0.2%. 3.6. Issues related to modelling of EAST results The simulations for modelling the radiation measured in the EAST facility are an idealised approximation of the actual tube flow phenomena. First, the simulations are based on an assumption that the flow is in equilibrium, with the post-shock conditions being calculated by CEA (Chemical Equilibrium with Applications) [31]. The reason for using equilibrium post-shock conditions is due to CFD computations for flight showing that the flow relaxes to an ‘‘equilibrium’’ state approximately 6 cm behind the normal shock, as seen in Fig. 4. Therefore, according to the CFD results, the flow region for most of the EAST shots that is deemed to show steady state radiance should nominally have reached equilibrium. It should be noted that there is some uncertainty regarding the rates and reaction mechanisms used in the CFD solution, which may affect the calculated relaxation to equilibrium. Fig. 4 shows the results of a computation performed on a hemisphere of 1 m radius, with the stagnation line taken as representative of the relaxation found in the flow behind the moving shock in EAST. A two-dimensional grid of size 160  245 (streamwise  normal) was constructed using the software, GridPro, with the grid being

Fig. 4. Relaxation of translational and vibrational temperature behind a shock at 6.5 km/s and 0.25 Torr.

large enough to accommodate the bow shock. Flow computations were performed using v4.02.2 of an inhouse code, DPLR [32]. A 16-species (CO2, CO, CO þ , C2, N2, O2, NO, NO þ , CN, C, C þ , N, O, O þ , Ar, and e  ) gas model was used in the computations; the reaction mechanism and rates associated with this model can be found in the work of Park [33]. In addition to chemical nonequilibrium, the flow field was assumed to be in thermal nonequilibrium as well. Consequently, a two-temperature (TT v ) model was used. In the two-temperature model employed, the translational and rotational modes of molecules are assumed to be in equilibrium with the temperature of the free electrons ðT ¼ T trans ¼ T rot ¼ T e Þ, and are distinct from the vibrational and electronic modes of the molecules ðT v ¼ T vib ¼ T elec Þ. The equilibrium state that is reached behind the shock from the CFD calculations is in good agreement with the thermodynamic equilibrium state predicted by CEA, as seen in Fig. 4. It is assumed that the stagnation-line flow near the shock is analogous to the flow in the shock tube. However, due to the nature of the shock tube environment (such as shock deceleration, wall contamination, boundary layer growth and length of test time), there is no guarantee that the EAST flow actually reaches thermodynamic equilibrium. Using this equilibrium assumption in the simulations could lead to discrepancies between the predicted and measured results. Further discrepancies could also arise due to the calculation not taking into account the effect of the boundary layer on the wall of the shock tube. Therefore, absorption in the boundary layer and radiation from recombined species are not accounted for in the analysis. A time-accurate 2-D/axisymmetric simulation of the facility would be required to address these issues. 4. EAST data The VUV region is a very difficult region to obtain spectral data due to the absorption of the emitted radiation by ambient oxygen below 190 nm. Therefore, the collection optics and spectrometer need to be located in a vacuum environment, and special windows are required to allow the transmission of data (UV-Silica for 4165 nm, Sapphire for 4 145 nm, and LiF or MgF2 for 4120 nm). The EAST experiments are one of the only sources for calibrated, spectrally and spatially resolved VUV spectra obtained in a shock tube facility for Mars entry relevant conditions. The main spectral feature of interest for this paper is the CO 4th Positive emission between 120 and 240 nm. However, as the VUV spectrometer is unable to cover the entire CO 4th Positive band in one shot at a suitable spectral resolution, the experiments have focused on the emission between 145 and 195 nm. Furthermore, a number of experiments were performed to capture the black body limited deep VUV spectra of CO 4th Positive while simultaneously capturing the ‘‘red side’’ tail of CO 4th Positive on the UV/Vis spectrometer. Fig. 5 shows the radiance integrated over the CO 4th Positive band emitting between 145 and 195 nm. The data shows five shots with a constant level of steady state radiance between 6 and 10 cm. All of these shots would be assigned an equilibrium rating of 4 (out of 5) according to the

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Fig. 5. Radiance integrated over CO 4th Positive from 145 to 195 nm versus distance at 0.25 Torr for EAST shots (a) 51–16 6.29 km/s, (b) 51–17 6.54 km/s, (c) 51–18 6.49 km/s, (d) 51–19 6.45 km/s and (e) 51–20 6.44 km/s.

classification specified by Brandis et al. [34]. The reason these shots are not given an equilibrium rating of 5 is due to the relatively significant level of noise found in the steady state regions. 5. Comparison of predictions and EAST Fig. 6 shows a comparison of EAST CO 4th Positive radiative intensity data with results generated by HyperRad and with the databases compiled by Rodio and Hassan, Babou et al. and da Silva and Dudeck. All four cases have been calculated using the CEA calculated equilibrium

temperature. Comparisons have been presented for two different spectrometer configurations. First, the CO 4th Positive is shown centred on the spectrometer showing emission from 145 to 195 nm, as seen in Fig. 6(a)–(d). Second, CO 4th Positive has been split across two spectrometers showing emission from 130 to 165 nm (VUV camera) and 190–230 nm (UV/Vis camera), as seen in Fig. 6(e) and (f). In all cases, a 3-point moving average has been applied to the EAST results obtained from the VUV camera to remove some of the pixel-to-pixel noise. The emission between 120 and 165 nm is almost completely limited by the black body curve. Therefore, the radiance in this spectral

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Fig. 6. Comparison of various databases and EAST for CO 4th Positive emission at 0.25 Torr using the CEA calculated equilibrium temperature.

range should be purely a function of temperature. From 165 to 195 nm, portions of the spectrum are black body-limited. Under the finite spectral resolution of the experimental measurements, these regions are smeared out to lie below the black body curve, but are still strongly impacted by the temperature due to self-absorption of the line peaks. The first observation that can be clearly seen from Fig. 6 is that the black body limited region of the spectrum is significantly under-predicted. This implies that the CEA equilibrium temperature is less than the actual flow

temperature. In particular, the impact can be seen across the spectral region between 145 and 160 nm for all the databases implemented. However, the CEA equilibrium properties do produce a good comparison with EAST between 170–195 nm and 190–230 nm with both the Babou et al. database and HyperRad for some conditions (see Fig. 6(b), (c) and (e)). However, the mismatch in the black body region suggests this agreement may be fortuitous. The only alternative explanation for this agreement would require a wavelength-dependent calibration

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error increasing the shorter wavelength side of the data. However, at this time, there is no evidence to support a wavelength dependent intensity calibration error. Calibration errors are estimated at no more than 22% and are most likely to be constant across the entire spectrum (independent of wavelength) and therefore would result in a constant increase or decrease of the data across all wavelengths. As the EAST data is limited by the black body curve between 130 and 155 nm, the temperature of each experiment can be extracted from the data by matching the slope and intensity of this portion of the spectrum. In order to match the black body limited portion of the spectrum, a methodology was developed to perform simulations using a temperature greater than the equilibrium value calculated by CEA. This methodology is as follows: 1. CEA is used to calculate the post shock conditions based on the experimentally measured shock speed, initial temperature and pressure of the test gas. 2. An initial guess of the black body temperature is obtained by fitting a black body curve to the upper limit of EAST data for wavelengths up to 155 nm. 3. This initial temperature is then used as a first guess for an iterative process using NEQAIR to obtain the best fit through the EAST data for wavelengths up to 155 nm. It should be noted that NEQAIR is only used to apply the experimentally measured spectral convolution function to the black body curve. 4. With the new experimental black body temperature, the post shock density of the flow is decreased by the same relative amount that the temperature of the flow was increased, thereby, maintaining the same pressure. 5. A new temperature-volume CEA calculation is performed using the updated flow density and temperature to calculate the new state of the post shock conditions.

Various permutations of this method have also been tried, such as running a temperature-pressure CEA calculation using both an assumption of constant pressure across the shock and also with increasing the pressure by the same relative amount as the temperature (therefore assuming a constant density). In all cases the mass fractions for all species agreed to within 5%. Furthermore, the mass fractions of species contributing to the majority of the heat flux for conditions relevant to this paper were in even closer agreement, CO (within 0.5%), CN (within 0.3%) and C2 (within 2%). The calculations performed with the black body temperature extracted from each EAST experiment are shown in Fig. 7, with the data arranged in the same manner as Fig. 6. The amount of temperature increase required for each shot is indicated in the caption. The temperature increase is not consistent from shot to shot, as shown in Fig. 8 and summarised in Table 1. Fig. 8 shows the per cent increase from equilibrium temperature to black body temperature for 11 shots from EAST at different shock speeds and initial pressures. The figure shows that there is no trend between the per cent increase in temperature and shock velocity. There could potentially be a trend suggesting the per cent increase in temperature increases with increasing pressure,

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as previously identified by Cruden et al. [1]. However, more shots at 1.0 Torr and 0.1 Torr would be required to verify this trend. Fig. 9 shows the variation of number densities for species that are significant to the total radiation for the conditions presented in this paper at a constant density of 0.01 kg/m3. It can be seen from this figure that a small increase in temperature can drastically change the number density of a species. For example, an increase in temperature from 5500 K to 6000 K, corresponds to an increase in C2 number density by a factor of 14. Fig. 10 shows a comparison of intensities with and without self-absorption at 6.44 km/s and 0.25 Torr with black body curves calculated at an equilibrium temperature of 5833 K and the increased temperature to match the black body limited portion of shot T51-20 (6158 K). From this figure it can be clearly seen how a small increase in temperature corresponds to a large increase in emitted radiation from CO 4th Positive. Fig. 7 shows that when using the Rodio and Hassan, and da Silva and Dudeck databases combined with increasing the temperature to match the black body limit, the overall agreement between the simulation and experiment is generally very good. However, there are a few discrepancies evident across all the conditions. These differences include an over-prediction of EAST between approximately 165–170 nm with both the Rodio and Hassan, and da Silva and Dudeck databases and an under-prediction of EAST between approximately 180– 195 nm with the Rodio and Hassan database. When using the Babou et al. database and HyperRad, even though the agreement is still maintained from 145 to 160 nm (the black body limited region), there is a substantial overprediction of EAST from 160 to 195 nm. A possible explanation for the over-prediction of these two databases would be justified if there were to be a nonboltzmann population of the high vibrational energy states of CO, thus affecting the transitions corresponding to the bands emitting from 160 nm and longer. Figs. 6(e), (f) and 7(e) and (f) show composite spectral images taken from both the VUV and UV/Vis cameras. These images allow a comparison of the shorter and longer wavelengths of CO 4th Positive. Furthermore, as these VUV experiments extend further into shorter wavelengths, it allows for a better black body temperature fit. These figures also include the black body curves calculated at the temperature extracted from the experimental result. EAST data is presented at two conditions for the composite images, 6.8 km/s (Figs. 6(e) and 7(e)) and 7.96 km/s (Figs. 6(f) and 7(f)) at 0.25 Torr. With the increased temperature, the Rodio and Hassan, and da Silva and Dudeck data show an under-prediction of the spectrum from 190 to 230 nm. The Babou et al. data and HyperRad, again show an over-prediction of the spectrum from 190 to 230 nm for the 6.8 km/s condition, see Fig. 7(e). However, both databases show very good agreement for the 7.96 km/s condition, see Fig. 7(f). The good agreement shown in Fig. 7(f) may be due to the radiance captured on the UV/Vis camera for this shot not reaching a clear steady-state value. It can also be seen from Figs. 6 and 7 that the two databases that use an experimental based ETMF (Rodio and Hassan, and da Silva and Dudeck) produce similar spectral results and show similar trends

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Fig. 7. Comparison of various databases and EAST for CO 4th Positive emission at 0.25 Torr using a temperature increase of (a) 460 K, (b) 278 K, (c) 125 K, (d) 325 K, (e) 240 K and (f) 374 K compared to CEA equilibrium.

when compared to the EAST data. Similar observations also apply to the results generated with the Babou et al. database and HyperRad when compared to EAST, both of which use an ETMF based on ab initio calculations. Fig. 11 shows a comparison of EAST data and all four databases at 0.1 Torr. For this particular shot, it appears that the CEA equilibrium calculated temperature captures the black body limited region of the spectra in EAST and therefore no temperature increase is required. The figure shows

that although all databases show an over-prediction when compared to EAST, both the Rodio and Hassan, and da Silva and Dudeck databases show relatively good agreement. At this lower pressure condition, nonequilibrium effects will become more significant. Therefore, the overprediction shown in this figure may be due to a nonboltzmann distribution of CO states. It should also be noted that there are further differences in the simulated CO 4th Positive optically thin

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Fig. 8. Per cent increase required to match experimental black body compared to CEA equilibrium.

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Fig. 9. Species number density as a function of temperature at 0.01 kg/m3.

Table 1 List of EAST shots used in this paper with corresponding CEA equilibrium temperature and the increase in temperature required to match the black body limited portion of the EAST spectrum. Shot no. Shock speed (km/s)

Pressure (Torr)

Temperature CEA increase to equilibrium (Temperature, K) match black body (K)

T48-16 T48-17 T48-27 T48-31 T48-40 T51-16 T51-17 T51-18 T51-19 T51-20 T51-26

1.0 1.0 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.10

6793 7160 6162 6169 6826 5625 5941 5890 5845 5833 6252

7.16 7.74 6.80 6.81 7.96 6.29 6.54 6.49 6.45 6.44 7.35

507 540 240 333 374 460 278 438 125 325 0

intensity across the various databases. Fig. 12 shows a comparison of the optically thin emission of CO 4th Positive calculated using the Rodio and Hassan, da Silva and Dudeck, Babou et al. and HyperRad databases. It can be seen that there are also significant discrepancies in the magnitude of the spectra for wavelengths shorter than 162 nm. However, as these wavelengths are completely black body limited, the transitions corresponding to the emission in these wavelengths can not be validated with these experiments.

Fig. 10. CO 4th Positive intensity calculated by NEQAIR using the Rodio and Hassan data with and without self-absorption (path length¼ 10.16 cm). 6.44 km/s and 0.25 Torr.

5.1. Validation of temperature increase In order to increase confidence in performing simulations using the black body temperature extracted from the EAST data, the influence of this temperature increase on the Vis/NIR and IR spectral data acquired from the same shots coinciding with the CO 4th Positive data has been analysed. Fig. 13(a) shows that the emission in the IR region is dominated by atomic C lines with a broad emission from CN Red. The results for the IR spectral region are shown in Fig. 13(b) and coincide with the CO 4th Positive data presented in Fig. 7(f) where a temperature increase of 374 K compared to equilibrium was

Fig. 11. Comparison of Rodio and Hassan, Babou et al., da Silva and Dudeck databases, HyperRad and EAST for CO 4th Positive emission at 0.1 Torr.

required to match the black body limited spectral region. It can be seen from the figure that there is a substantial improvement in terms of the agreement with EAST when

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the temperature increase is implemented. When the temperature of the flow is increased, the simulation agrees to within 10%, whereas the equilibrium solution is lower by a factor of 2.1. The effect of the temperature increase on the simulations for the Vis/NIR spectral region (dominated by emission from C2 Swan and CN Red, as depicted in Fig. 14(a)) is shown in Fig. 14. In all cases the integrated radiance is closer to the experimental result when the temperature is increased. Fig. 14(b)–(d) shows that when the temperature is increased, although the agreement is improved for the 575–875 nm (CN Red) region compared to equilibrium, there is still substantial room for improvement. The disagreement in this spectral region has also been observed by Cruden et al. [1]. However, in contrast, the C2 Swan bands between 475 and 575 nm are very well matched when the temperature is increased, as shown in Fig. 14(b)–(d). It can also be seen in these figures that the agreement of the atomic Oxygen line at 777 nm shows greatly improved agreement with EAST when using the increased temperature in the simulations. This is particularly evident in Fig. 14(b)–(d). Results are not shown for EAST shots T51-16 and T51-19 as the C2 Swan

Fig. 12. Calculation showing optically thin intensities calculated with the Rodio and Hassan, Babou et al. and da Silva and Dudeck databases at 6.45 km/s and 0.25 Torr.

emission does not reach a steady state behind the shock, whereas shots T51-17, T51-18 and T51-20 do. There is presently no data available where deep VUV CO 4th Positive and CN Violet spectra were taken from the same shot. Therefore, the influence of a temperature increase corresponding to the black body limited region of EAST on the CN Violet emission can not be made directly. However, as Fig. 8 showed, the average temperature increase implemented was approximately 5% with a maximum temperature increase of approximately 10%. Therefore, the influences of a 5% and 10% increase from the nominal CEA calculated temperature can be compared to the UV/Vis spectra obtained from EAST. This spectral region is dominated by emission of CN Violet with relatively small amounts of C2 Swan, as shown in Fig. 15(a). Fig. 15(b) shows that by using the CEA equilibrium temperature, the simulated result is significantly less than the experimental data, therefore a temperature increase would be required to improve the agreement. Increasing the temperature by 5% results in very good agreement between the EAST data and NEQAIR for the C2 Swan band, however, over-predicts the CN Violet magnitude. A more appropriate temperature increase would be less than 5%, however the result suggests that nonequilibrium compositions would be required at this increased temperature to match the data exactly. Fig. 15(c) again shows that using the CEA equilibrium temperature significantly under-predicts the EAST result (by a factor of 2.1 in this case). When the temperature is increased by 10%, the agreement between EAST and NEQAIR for CN Violet is excellent, within 2%. However, the figure also shows that using the increased temperature over-predicts the C2 Swan radiation. Fig. 15(d) shows minimal difference in the CN Violet spectrum as the increase in emission due to the temperature increase has been offset by the CN molecule beginning to dissociate. However, the increased temperature result shows improved agreement for the C2 Swan band. When the equilibrium temperature is used, the integrated radiance is calculated to be 20% less than EAST. However, when the temperature increase is implemented, the agreement is improved to within 9.5%. Fig. 16 shows the radiance from

Fig. 13. (a) NEQAIR calculation showing main radiators for the IR spectral region at 7.96 km/s and 0.25 Torr and (b) comparison of NEQAIR and EAST for the Infra-Red spectral region at 0.25 Torr.

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Fig. 14. (a) NEQAIR calculation showing main radiators for the Vis/NIR spectral region at 6.45 km/s. Comparison of NEQAIR and EAST for the Vis/NIR spectral region at 0.25 Torr, (b) 6.54 km/s, (c) 6.49 km/s and (d) 6.44 km/s.

the UV/Vis spectrometer integrated over 330–500 nm and shows that for each shot, the EAST data supports an increase in temperature used in the simulations by a similar percentage as was shown in Fig. 8. 5.2. Summary of results Fig. 17 summarises the comparisons of CO 4th Positive radiance integrated over 145–195 nm using the CEA equilibrium temperature (Fig. 17(a) and detailed in Table 2) and using the black body temperature extracted from EAST (Fig. 17(b) and detailed in Table 3). Fig. 17(a) shows that for four of the EAST shots, all databases significantly under-predict the integrated experimental result when the equilibrium temperature is used. The one data point that agrees with prediction appears to be an outlier, as does one data point which significantly exceeds the other radiances. However, when the temperature is increased to match the black body limited portion of the EAST spectra, as shown in Fig. 17(b), the databases bound the experimental result. It can also be seen from these figures that the two databases that use an experimental based ETMF (Rodio and Hassan, and da Silva and Dudeck) produce a smaller integrated value of radiance when compared to HyperRad and Babou et al., both of which use an ETMF based on ab initio calculations. Fig. 17(b) also shows the results of an analysis related to the uncertainty

in temperature due to the calculation of shock speed for each shot. Each data point shown in the figure shows the percentage temperature increase used in the calculations and next to this number in parentheses is the corresponding uncertainty in temperature due to the uncertainty in the measurement of the shock speed, using an estimated shock speed uncertainty of 1%. The uncertainty in temperature due to shock speed is around 1–1.5%, while the uncertainty in temperature due to the absolute radiance calibrations is approximately 1.5%. The temperature mismatch however, varies from 2 to 9%, so may only partly be explained by these experimental uncertainties. Furthermore, these experimental errors are expected to be normally distributed while the temperature trend shows a bias towards a higher temperature. This, in combination with the discussion of Section 5.1, suggests the temperature increase is a real phenomenon in the shock tube. Potential theories for this increase relate to either the driver gas heating the test gas, viscous flow effects causing the deceleration of the shock or expansion waves originating at the driver impinging on the test gas. However, reasons for this are not yet fully understood. 6. Conclusion Measurements of CO 4th Positive radiative intensity have been made across a range of conditions in the EAST

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Fig. 15. (a) NEQAIR calculation showing main radiators for the UV/Vis spectral region at 6.60 km/s. Comparison of NEQAIR and EAST for the UV/Vis spectral region at 0.25 Torr at (b) 6.43 km/s (c) 6.60 km/s and (d) 7.75 km/s.

Fig. 16. Summary of comparisons showing the influence on intensity of 5% and 10% increases in CEA equilibrium temperature.

facility with the results being compared against four CO 4th Positive databases compiled and calculated by Rodio and Hassan, Babou et al., da Silva and Dudeck and HyperRad. Initial comparisons were conducted using equilibrium conditions as calculated by CEA. However, it has been shown in this paper that the predicted equilibrium temperature significantly under-predicts the EAST data, in particular, the spectral region of EAST where the intensity

is limited by the black body curve. This spectral region should purely be a function of temperature and has been shown to be under-predicted for all the 0.25 Torr conditions presented in this paper where spectral information is available below 155 nm. As the intensity measured on EAST in the spectral region from 130 to 155 nm is limited by the black body curve, it enables a relatively accurate measurement of the experimental flow temperature. This temperature was found to be 2–9% higher than the CEA equilibrium calculated value. Therefore calculations were performed with both the black body temperature extracted from each EAST shot and at the equilibrium value. Overall, the simulations performed at equilibrium under-predict the experiment by an average of approximately 40%. When the simulations use the increased temperature extracted from the black body limited radiation from EAST, the results agree on average within approximately 15%. The need for the temperature increase in experiment has been further validated by comparing the influence of the increase in temperature for other spectral regions. Results from comparisons conducted in the UV/Vis, Vis/NIR and IR spectral regions have shown that the calculations performed with an increased temperature offer improved agreement with the EAST data, particularly when the integrated radiance is compared. By using the extracted temperature from the black body

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limited spectral region in the EAST data, greatly improved agreement with simulations has been observed for radiation emitted by CO 4th Positive, C2 Swan, CN Violet, atomic O and atomic C. Better agreement was observed for CN Red, however there is still room for improvement in terms of the comparison with EAST data. It was also found that CO 4th Positive databases derived from DeLeon’s ETMF agreed well with experiment when temperature was adjusted to match the black body limited region. Furthermore, these databases showed better agreement at 0.1 Torr where the temperature agreed well with the equilibrium prediction. The ab initio based ETMF’s yielded higher radiances than that of DeLeon at all conditions. However, a possible nonboltzmann distribution of CO states could contribute to this over-prediction. 7. Future work

Fig. 17. Summary of the comparison of the various databases and EAST for CO 4th Positive emission at 0.25 Torr at (a) equilibrium temperature (b) experimental black body temperature (also showing percent increase in equilibrium temperature, and corresponding uncertainty in temperature due to the uncertainty in shock speed).

Future experiments covering the shorter wavelengths of CO 4th Positive on the VUV camera to enable the extraction of the black body temperature while simultaneously capturing the CN Violet emission on the UV/Vis camera would be highly valuable for improved statistics and validation of the increase in temperature. These experiments could also focus on expanding the test condition envelope to better enable the extraction of trends in the data against shock velocity and initial pressure. If possible, obtaining data from EAST that would enable an estimate of the electron number density to be calculated may provide useful information to assess the level of equilibrium that the flow is reaching. Furthermore, this information may help provide insights into the under-prediction of the CN Red spectrum. The results may also prompt an analysis to determine the effect of nonequilibrium in electronically excited states, and the subsequent impact on the radiation calculation. With

Table 2 Summary of CO 4th positive comparisons calculated using equilibrium temperatures. Shot no.

T51-16 T51-17 T51-18 T51-19 T51-20

Shock speed (km/s)

6.29 6.54 6.49 6.45 6.44

EAST

0.990 1.352 1.642 0.756 1.201

Radiance: 145–195 nm, W/cm2 sr (per cent difference w.r.t. EAST) Gas state

Rodio et al.

Babou et al.

da Silva et al.

HyperRad

CEA CEA CEA CEA CEA

0.285 0.674 0.589 0.523 0.507

0.455 1.069 0.935 0.832 0.807

0.343 0.810 0.708 0.629 0.610

0.398 0.931 0.815 0.726 0.704

Average difference:

(  71%) (  50%) (  64%) (  31%) (  58%)

 55%

(  54%) (  21%) (  43%) (10%) (  33%)

 28%

( 65%) (  40%) (  57%) ( 17%) (  49%)

 46%

( 60%) ( 31%) ( 50%) ( 4%) ( 41%)

 37%

Table 3 Summary of CO 4th positive comparisons calculated using extracted black body temperatures. Shot no.

T51-16 T51-17 T51-18 T51-19 T51-20

Shock speed (km/s)

6.29 6.54 6.49 6.45 6.44

EAST

0.990 1.352 1.642 0.756 1.201

Radiance: 145–195 nm, W/cm2 sr (per cent difference w.r.t. EAST) Gas state (K)

Rodio et al.

Babou et al.

da Silva et al.

HyperRad

CEA þ460 CEA þ278 CEA þ438 CEA þ125 CEA þ325

0.920 1.279 1.592 0.715 1.106

1.462 2.025 2.523 1.135 1.753

1.110 1.541 1.922 0.860 1.333

1.269 1.749 2.169 0.988 1.518

Average difference:

 6%

(  7%) ( 5%) ( 3%) ( 5%) ( 8%)

49%

(48%) (50%) (54%) (50%) (46%)

14%

(12%) (14%) (17%) (14%) (11%)

29%

(28%) (29%) (32%) (31%) (26%)

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